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Question

# Two satellites A and B, have ratio of masses 3:1 are in circular orbits of radii r and 4r. Then ratio of total mechanical energy of A and B is

A
1:3
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B
3:1
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C
3:4
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D
12:1
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Solution

## The correct option is D 12:1The total mechanical energy of a satellite of mass m in a circular orbit of radius r around a planet of mass M is given by E=−GMm2r So, E∝mr Given, Ratio of the masses of the satellites, mAmB=31 Ratio of the orbits of the satellites, rArB=r4r=14 Now, the ratio of the total meachanical energy, EAEB=mAmB×rBrA ⇒EAEB=31×41 ⇒EAEB=12:1 Hence, option (d) is the correct answer.

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